Question 109
Let $\triangle ABC$ be an acute triangle, and let $M$ be the midpoint of $AC$. A circle $\omega$ passing through $B$ and $M$ meets the sides $AB$ and $BC$ again at $P$ and $Q$, respectively. Let $T$ be the point such that the quadrilateral $BPTQ$ is a parallelogram. Suppose that $T$ lies on the circumcircle of the triangle $ABC$. Determine all possible values of $BT/BM$.